66:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Sistemas de ecuaciones:@0.073089:0.043661:0.282490:0.043661:0.282490:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.3 Demostración de propiedades de la adición de M [ ]:@0.293660:0.140040:0.747163:0.140040:0.747163:0.123093:0.293660:0.123093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2×2:@0.705191:0.143212:0.723005:0.143212:0.723005:0.133332:0.705191:0.133332:0.000000:0.000000:0.000000
ℝ:@0.728424:0.140622:0.741714:0.140622:0.741714:0.122968:0.728424:0.122968:0.000000
Demostraremos la propiedad iii. El resto queda como tarea.:@0.293663:0.170980:0.721709:0.170980:0.721709:0.154546:0.293663:0.154546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea A = :@0.293663:0.205914:0.352891:0.205914:0.352891:0.189480:0.293663:0.189480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.359928:0.196032:0.368345:0.196032:0.368345:0.181117:0.359928:0.181117:0.000000
11:@0.368285:0.198916:0.377768:0.198916:0.377768:0.190206:0.368285:0.190206:0.000000:0.000000
a:@0.393409:0.196032:0.401826:0.196032:0.401826:0.181117:0.393409:0.181117:0.000000
12:@0.401766:0.198916:0.411249:0.198916:0.411249:0.190206:0.401766:0.190206:0.000000:0.000000
a:@0.359928:0.217473:0.368345:0.217473:0.368345:0.202559:0.359928:0.202559:0.000000
21:@0.368285:0.220359:0.377768:0.220359:0.377768:0.211649:0.368285:0.211649:0.000000:0.000000
a:@0.393409:0.217473:0.401826:0.217473:0.401826:0.202559:0.393409:0.202559:0.000000
22:@0.401766:0.220359:0.411249:0.220359:0.411249:0.211649:0.401766:0.211649:0.000000:0.000000
 una matriz de :@0.417938:0.205914:0.525907:0.205914:0.525907:0.189480:0.417938:0.189480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M:@0.525734:0.205914:0.539613:0.205914:0.539613:0.189508:0.525734:0.189508:0.000000
2×2:@0.539546:0.209086:0.556330:0.209086:0.556330:0.199505:0.539546:0.199505:0.000000:0.000000:0.000000
[ ].:@0.556275:0.205914:0.582284:0.205914:0.582284:0.189480:0.556275:0.189480:0.000000:0.000000:0.000000:0.000000
ℝ:@0.561079:0.206496:0.574369:0.206496:0.574369:0.188842:0.561079:0.188842:0.000000
iii. :@0.293660:0.248892:0.314000:0.248892:0.314000:0.232223:0.293660:0.232223:0.000000:0.000000:0.000000:0.000000:0.000000
Existencia de elemento neutro. La matriz 0  = :@0.323858:0.248892:0.666331:0.248892:0.666331:0.232223:0.323858:0.232223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.675714:0.238117:0.683881:0.238117:0.683881:0.223177:0.675714:0.223177:0.000000
0:@0.704446:0.238117:0.712613:0.238117:0.712613:0.223177:0.704446:0.223177:0.000000
0:@0.675714:0.259562:0.683881:0.259562:0.683881:0.244622:0.675714:0.244622:0.000000
0:@0.704446:0.259562:0.712613:0.259562:0.712613:0.244622:0.704446:0.244622:0.000000
 pertenece:@0.721776:0.248892:0.803158:0.248892:0.803158:0.232223:0.721776:0.232223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.323781:0.279830:0.336096:0.279830:0.336096:0.263396:0.323781:0.263396:0.000000:0.000000
M:@0.336004:0.279830:0.349883:0.279830:0.349883:0.263424:0.336004:0.263424:0.000000
2×2:@0.349821:0.283002:0.366605:0.283002:0.366605:0.273421:0.349821:0.273421:0.000000:0.000000:0.000000
[ ] y como :@0.366550:0.279830:0.451904:0.279830:0.451904:0.263396:0.366550:0.263396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.371354:0.280412:0.384644:0.280412:0.384644:0.262758:0.371354:0.262758:0.000000
a  :@0.451775:0.279830:0.468514:0.279830:0.468514:0.263424:0.451775:0.263424:0.000000:0.000000:0.000000
ij:@0.460952:0.283002:0.465234:0.283002:0.465234:0.273438:0.460952:0.273438:0.000000:0.000000
∈:@0.468440:0.279414:0.481565:0.279414:0.481565:0.262425:0.468440:0.262425:0.000000
  , se tiene   + 0 = 0 +   = 0,     = 1, 2,   = 1, 2. Entonces, :@0.481473:0.279830:0.892746:0.279830:0.892746:0.263396:0.481473:0.263396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.485430:0.280412:0.498720:0.280412:0.498720:0.262758:0.485430:0.262758:0.000000
a:@0.566091:0.279830:0.575350:0.279830:0.575350:0.263424:0.566091:0.263424:0.000000
ij:@0.575278:0.283002:0.579560:0.283002:0.579560:0.273438:0.575278:0.273438:0.000000:0.000000
a:@0.653706:0.279830:0.662965:0.279830:0.662965:0.263424:0.653706:0.263424:0.000000
ij:@0.662896:0.283002:0.667178:0.283002:0.667178:0.273438:0.662896:0.273438:0.000000:0.000000
i:@0.709811:0.279830:0.713603:0.279830:0.713603:0.263424:0.709811:0.263424:0.000000
j:@0.764278:0.279830:0.767905:0.279830:0.767905:0.263424:0.764278:0.263424:0.000000
A:@0.323774:0.314764:0.333659:0.314764:0.333659:0.298358:0.323774:0.298358:0.000000
 + 0 =  :@0.333585:0.314764:0.384150:0.314764:0.384150:0.298330:0.333585:0.298330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.391198:0.304885:0.399616:0.304885:0.399616:0.289970:0.391198:0.289970:0.000000
11:@0.399555:0.307769:0.409038:0.307769:0.409038:0.299059:0.399555:0.299059:0.000000:0.000000
a:@0.424680:0.304885:0.433097:0.304885:0.433097:0.289970:0.424680:0.289970:0.000000
12:@0.433037:0.307769:0.442519:0.307769:0.442519:0.299059:0.433037:0.299059:0.000000:0.000000
a:@0.391198:0.326327:0.399616:0.326327:0.399616:0.311413:0.391198:0.311413:0.000000
21:@0.399555:0.329211:0.409038:0.329211:0.409038:0.320502:0.399555:0.320502:0.000000:0.000000
a:@0.424680:0.326327:0.433097:0.326327:0.433097:0.311413:0.424680:0.311413:0.000000
22:@0.433037:0.329211:0.442519:0.329211:0.442519:0.320502:0.433037:0.320502:0.000000:0.000000
  + :@0.449206:0.314766:0.472050:0.314766:0.472050:0.298333:0.449206:0.298333:0.000000:0.000000:0.000000:0.000000
0:@0.481576:0.305777:0.489743:0.305777:0.489743:0.290837:0.481576:0.290837:0.000000
0:@0.510308:0.305777:0.518475:0.305777:0.518475:0.290837:0.510308:0.290837:0.000000
0:@0.481576:0.327223:0.489743:0.327223:0.489743:0.312283:0.481576:0.312283:0.000000
0:@0.510308:0.327223:0.518475:0.327223:0.518475:0.312283:0.510308:0.312283:0.000000
  =  :@0.527635:0.314766:0.554436:0.314766:0.554436:0.298333:0.527635:0.298333:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.564305:0.304885:0.572722:0.304885:0.572722:0.289970:0.564305:0.289970:0.000000
11:@0.572662:0.307769:0.582145:0.307769:0.582145:0.299059:0.572662:0.299059:0.000000:0.000000
 + 0:@0.582098:0.304885:0.607367:0.304885:0.607367:0.289945:0.582098:0.289945:0.000000:0.000000:0.000000:0.000000
a:@0.628619:0.304885:0.637036:0.304885:0.637036:0.289970:0.628619:0.289970:0.000000
12:@0.636975:0.307769:0.646458:0.307769:0.646458:0.299059:0.636975:0.299059:0.000000:0.000000
 + 0:@0.646412:0.304885:0.671680:0.304885:0.671680:0.289945:0.646412:0.289945:0.000000:0.000000:0.000000:0.000000
a:@0.564299:0.326330:0.572716:0.326330:0.572716:0.311415:0.564299:0.311415:0.000000
21:@0.572662:0.329211:0.582145:0.329211:0.582145:0.320502:0.572662:0.320502:0.000000:0.000000
 + 0:@0.582098:0.326327:0.607367:0.326327:0.607367:0.311388:0.582098:0.311388:0.000000:0.000000:0.000000:0.000000
a:@0.628619:0.326327:0.637036:0.326327:0.637036:0.311413:0.628619:0.311413:0.000000
22:@0.636975:0.329211:0.646458:0.329211:0.646458:0.320502:0.636975:0.320502:0.000000:0.000000
 + 0:@0.646412:0.326327:0.671680:0.326327:0.671680:0.311388:0.646412:0.311388:0.000000:0.000000:0.000000:0.000000
  =  :@0.681166:0.314766:0.707967:0.314766:0.707967:0.298333:0.681166:0.298333:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.715022:0.304885:0.723439:0.304885:0.723439:0.289970:0.715022:0.289970:0.000000
11:@0.723379:0.307769:0.732862:0.307769:0.732862:0.299059:0.723379:0.299059:0.000000:0.000000
a:@0.748503:0.304885:0.756920:0.304885:0.756920:0.289970:0.748503:0.289970:0.000000
12:@0.756860:0.307769:0.766343:0.307769:0.766343:0.299059:0.756860:0.299059:0.000000:0.000000
a:@0.715022:0.326327:0.723439:0.326327:0.723439:0.311413:0.715022:0.311413:0.000000
21:@0.723379:0.329211:0.732862:0.329211:0.732862:0.320502:0.723379:0.320502:0.000000:0.000000
a:@0.748503:0.326327:0.756920:0.326327:0.756920:0.311413:0.748503:0.311413:0.000000
22:@0.756860:0.329211:0.766343:0.329211:0.766343:0.320502:0.756860:0.320502:0.000000:0.000000
  =  . :@0.773032:0.314766:0.812818:0.314766:0.812818:0.298333:0.773032:0.298333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.795773:0.314766:0.805658:0.314766:0.805658:0.298360:0.795773:0.298360:0.000000
Conclusión:   + 0 =  . De manera similar, se prueba que 0 +   =  .:@0.323774:0.352848:0.800283:0.352848:0.800283:0.336415:0.323774:0.336415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.412332:0.352848:0.422216:0.352848:0.422216:0.336442:0.412332:0.336442:0.000000
A:@0.468621:0.352848:0.478506:0.352848:0.478506:0.336442:0.468621:0.336442:0.000000
A:@0.758664:0.352848:0.768549:0.352848:0.768549:0.336442:0.758664:0.336442:0.000000
A:@0.787269:0.352848:0.797154:0.352848:0.797154:0.336442:0.787269:0.336442:0.000000
5.4 Resta de matrices:@0.293623:0.387353:0.459209:0.387353:0.459209:0.370406:0.293623:0.370406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición  :@0.293623:0.414715:0.381592:0.414715:0.381592:0.397768:0.293623:0.397768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.374652:0.414715:0.377855:0.414715:0.377855:0.398281:0.374652:0.398281:0.000000
Sean  ,     :@0.381518:0.414715:0.467590:0.414715:0.467590:0.398281:0.381518:0.398281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.420928:0.414715:0.446643:0.414715:0.446643:0.398308:0.420928:0.398308:0.000000:0.000000:0.000000
∈:@0.450527:0.414298:0.463651:0.414298:0.463651:0.397310:0.450527:0.397310:0.000000
M:@0.467517:0.414715:0.481396:0.414715:0.481396:0.398308:0.467517:0.398308:0.000000
2×2 :@0.481354:0.417897:0.500445:0.417897:0.500445:0.408316:0.481354:0.408316:0.000000:0.000000:0.000000:0.000000
[ ]. Se define la matriz   –   como:   –   =   + (– ).:@0.500385:0.414725:0.869782:0.414725:0.869782:0.398291:0.500385:0.398291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.505190:0.415307:0.518480:0.415307:0.518480:0.397653:0.505190:0.397653:0.000000
A B:@0.666934:0.414725:0.702607:0.414725:0.702607:0.398319:0.666934:0.398319:0.000000:0.000000:0.000000
A B:@0.756099:0.414725:0.791772:0.414725:0.791772:0.398319:0.756099:0.398319:0.000000:0.000000:0.000000
A:@0.810492:0.414725:0.820377:0.414725:0.820377:0.398319:0.810492:0.398319:0.000000
B:@0.853013:0.414725:0.861849:0.414725:0.861849:0.398319:0.853013:0.398319:0.000000
Ejercicio 4:@0.293617:0.442087:0.370761:0.442087:0.370761:0.425417:0.293617:0.425417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.293660:0.474345:0.310668:0.474345:0.310668:0.457676:0.293660:0.457676:0.000000:0.000000:0.000000
Sean:@0.323858:0.474345:0.359414:0.474345:0.359414:0.457911:0.323858:0.457911:0.000000:0.000000:0.000000:0.000000
 A = :@0.359310:0.474345:0.389811:0.474345:0.389811:0.457939:0.359310:0.457939:0.000000:0.000000:0.000000:0.000000:0.000000
2 8:@0.401806:0.464464:0.433718:0.464464:0.433718:0.449524:0.401806:0.449524:0.000000:0.000000:0.000000
–1 4:@0.397673:0.485909:0.433718:0.485909:0.433718:0.470969:0.397673:0.470969:0.000000:0.000000:0.000000:0.000000
 , B = :@0.446397:0.474345:0.482346:0.474345:0.482346:0.457939:0.446397:0.457939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 –2:@0.493533:0.463570:0.532439:0.463570:0.532439:0.448630:0.493533:0.448630:0.000000:0.000000:0.000000:0.000000
–3 –1:@0.489383:0.485015:0.532439:0.485015:0.532439:0.470075:0.489383:0.470075:0.000000:0.000000:0.000000:0.000000:0.000000
 . :@0.538025:0.474345:0.547836:0.474345:0.547836:0.457939:0.538025:0.457939:0.000000:0.000000:0.000000
Entonces:@0.547784:0.474345:0.614945:0.474345:0.614945:0.457911:0.547784:0.457911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, –B = :@0.614823:0.474345:0.656663:0.474345:0.656663:0.457939:0.614823:0.457939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–5 2:@0.664043:0.463570:0.700807:0.463570:0.700807:0.448630:0.664043:0.448630:0.000000:0.000000:0.000000:0.000000
3 1:@0.668193:0.485015:0.700807:0.485015:0.700807:0.470075:0.668193:0.470075:0.000000:0.000000:0.000000
, :@0.712341:0.474345:0.718913:0.474345:0.718913:0.457939:0.712341:0.457939:0.000000:0.000000
y:@0.718854:0.474345:0.726953:0.474345:0.726953:0.457911:0.718854:0.457911:0.000000
 :@0.293660:0.520898:0.297691:0.520898:0.297691:0.504464:0.293660:0.504464:0.000000
A B:@0.353902:0.520898:0.389575:0.520898:0.389575:0.504492:0.353902:0.504492:0.000000:0.000000:0.000000
 –   =   + (– ) = :@0.363713:0.520898:0.483268:0.520898:0.483268:0.504464:0.363713:0.504464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.408295:0.520898:0.418180:0.520898:0.418180:0.504492:0.408295:0.504492:0.000000
B:@0.450816:0.520898:0.459652:0.520898:0.459652:0.504492:0.450816:0.504492:0.000000
2 8:@0.493317:0.511015:0.523321:0.511015:0.523321:0.496075:0.493317:0.496075:0.000000:0.000000:0.000000
–1 4:@0.489167:0.532461:0.523321:0.532461:0.523321:0.517521:0.489167:0.517521:0.000000:0.000000:0.000000:0.000000
 + :@0.534136:0.520898:0.553022:0.520898:0.553022:0.504464:0.534136:0.504464:0.000000:0.000000:0.000000
–5 2:@0.561039:0.511909:0.594958:0.511909:0.594958:0.496969:0.561039:0.496969:0.000000:0.000000:0.000000:0.000000
3 1:@0.565189:0.533354:0.594958:0.533354:0.594958:0.518415:0.565189:0.518415:0.000000:0.000000:0.000000
 = :@0.604781:0.520898:0.623667:0.520898:0.623667:0.504464:0.604781:0.504464:0.000000:0.000000:0.000000
2 – 5:@0.634460:0.510121:0.666221:0.510121:0.666221:0.495182:0.634460:0.495182:0.000000:0.000000:0.000000:0.000000:0.000000
8 + 2:@0.686118:0.510121:0.719485:0.510121:0.719485:0.495182:0.686118:0.495182:0.000000:0.000000:0.000000:0.000000:0.000000
–1 + 3 4 + 1:@0.631197:0.531567:0.719485:0.531567:0.719485:0.516627:0.631197:0.516627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.725235:0.520898:0.744121:0.520898:0.744121:0.504464:0.725235:0.504464:0.000000:0.000000:0.000000
–3 10:@0.752849:0.511015:0.792709:0.511015:0.792709:0.496075:0.752849:0.496075:0.000000:0.000000:0.000000:0.000000:0.000000
2 5:@0.756982:0.532461:0.788643:0.532461:0.788643:0.517521:0.756982:0.517521:0.000000:0.000000:0.000000
. :@0.800624:0.520898:0.807858:0.520898:0.807858:0.504464:0.800624:0.504464:0.000000:0.000000
5.4 Producto de escalares por matrices:@0.293660:0.572050:0.595504:0.572050:0.595504:0.555104:0.293660:0.555104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A los elementos de   los denominamos escalares.:@0.293660:0.599412:0.656436:0.599412:0.656436:0.582979:0.293660:0.582979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.436390:0.599995:0.449680:0.599995:0.449680:0.582341:0.436390:0.582341:0.000000
Definición:@0.293660:0.626774:0.374781:0.626774:0.374781:0.609827:0.293660:0.609827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.374689:0.626774:0.377892:0.626774:0.377892:0.610341:0.374689:0.610341:0.000000
 :@0.377818:0.626774:0.381628:0.626774:0.381628:0.609827:0.377818:0.609827:0.000000
Sea       y   = ( )    :@0.381555:0.626774:0.558161:0.626777:0.558161:0.610343:0.381555:0.610341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.411172:0.626774:0.418793:0.626774:0.418793:0.610368:0.411172:0.610368:0.000000
∈:@0.422677:0.626358:0.435801:0.626358:0.435801:0.609370:0.422677:0.609370:0.000000
ℝ:@0.439666:0.627357:0.452956:0.627357:0.452956:0.609703:0.439666:0.609703:0.000000
A:@0.468787:0.626774:0.478671:0.626774:0.478671:0.610368:0.468787:0.610368:0.000000
a:@0.502177:0.626774:0.511436:0.626774:0.511436:0.610368:0.502177:0.610368:0.000000
ij:@0.511366:0.629949:0.515648:0.629949:0.515648:0.620385:0.511366:0.620385:0.000000:0.000000
2×2:@0.520411:0.629949:0.537195:0.629949:0.537195:0.620368:0.520411:0.620368:0.000000:0.000000:0.000000
∈:@0.541097:0.626361:0.554221:0.626361:0.554221:0.609372:0.541097:0.609372:0.000000
M:@0.558087:0.626777:0.571966:0.626777:0.571966:0.610371:0.558087:0.610371:0.000000
2×2:@0.571884:0.629949:0.588668:0.629949:0.588668:0.620368:0.571884:0.620368:0.000000:0.000000:0.000000
[ ]. Se define   como::@0.588613:0.626777:0.756818:0.626777:0.756818:0.610343:0.588613:0.610343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.593417:0.627359:0.606707:0.627359:0.606707:0.609705:0.593417:0.609705:0.000000
λA:@0.689706:0.626777:0.707137:0.626777:0.707137:0.610371:0.689706:0.610371:0.000000:0.000000
                           λA:@0.293674:0.650561:0.398576:0.650561:0.398576:0.634155:0.293674:0.634155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =  ( )  = (:@0.398705:0.650561:0.488496:0.650566:0.488496:0.634132:0.398705:0.634127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ a:@0.417499:0.650561:0.439109:0.650561:0.439109:0.634155:0.417499:0.634155:0.000000:0.000000:0.000000
ij:@0.439034:0.653738:0.443316:0.653738:0.443316:0.644174:0.439034:0.644174:0.000000:0.000000
2×2:@0.448079:0.653738:0.464862:0.653738:0.464862:0.644157:0.448079:0.644157:0.000000:0.000000:0.000000
λa:@0.488385:0.650566:0.505191:0.650566:0.505191:0.634160:0.488385:0.634160:0.000000:0.000000
ij:@0.505141:0.653738:0.509423:0.653738:0.509423:0.644174:0.505141:0.644174:0.000000:0.000000
):@0.509388:0.650566:0.514266:0.650566:0.514266:0.634132:0.509388:0.634132:0.000000
2×2:@0.514186:0.653738:0.530970:0.653738:0.530970:0.644157:0.514186:0.644157:0.000000:0.000000:0.000000
El producto de un número real   por una matriz     :@0.293660:0.677929:0.656780:0.677929:0.656780:0.661495:0.293660:0.661495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.510884:0.677929:0.518505:0.677929:0.518505:0.661523:0.510884:0.661523:0.000000
A:@0.627052:0.677929:0.636937:0.677929:0.636937:0.661523:0.627052:0.661523:0.000000
∈:@0.639956:0.677513:0.653080:0.677513:0.653080:0.660524:0.639956:0.660524:0.000000
M:@0.656062:0.677929:0.669941:0.677929:0.669941:0.661523:0.656062:0.661523:0.000000
2×2:@0.669667:0.681101:0.686172:0.681101:0.686172:0.671520:0.669667:0.671520:0.000000:0.000000:0.000000
[ ] es otra matriz de :@0.685991:0.677929:0.830929:0.677929:0.830929:0.661495:0.685991:0.661495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.690556:0.678512:0.703846:0.678512:0.703846:0.660857:0.690556:0.660857:0.000000
M:@0.830230:0.677929:0.844109:0.677929:0.844109:0.661523:0.830230:0.661523:0.000000
2×2:@0.843819:0.681101:0.860324:0.681101:0.860324:0.671520:0.843819:0.671520:0.000000:0.000000:0.000000
[ ] cuyos :@0.860143:0.677929:0.930938:0.677929:0.930938:0.661495:0.860143:0.661495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.864708:0.678512:0.877998:0.678512:0.877998:0.660857:0.864708:0.660857:0.000000
componentes son el producto de   por los respectivos componentes de la matriz  .:@0.293660:0.694571:0.885030:0.694571:0.885030:0.678137:0.293660:0.678137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.535716:0.694571:0.543336:0.694571:0.543336:0.678165:0.535716:0.678165:0.000000
A:@0.872200:0.694571:0.882085:0.694571:0.882085:0.678165:0.872200:0.678165:0.000000
Así, si A = :@0.293642:0.726828:0.365938:0.726828:0.365938:0.710395:0.293642:0.710395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.372970:0.716053:0.381387:0.716053:0.381387:0.701138:0.372970:0.701138:0.000000
11:@0.381326:0.718937:0.390808:0.718937:0.390808:0.710227:0.381326:0.710227:0.000000:0.000000
a:@0.406450:0.716053:0.414867:0.716053:0.414867:0.701138:0.406450:0.701138:0.000000
12:@0.414807:0.718937:0.424289:0.718937:0.424289:0.710227:0.414807:0.710227:0.000000:0.000000
a:@0.372970:0.737494:0.381387:0.737494:0.381387:0.722580:0.372970:0.722580:0.000000
21:@0.381326:0.740378:0.390808:0.740378:0.390808:0.731668:0.381326:0.731668:0.000000:0.000000
a:@0.406450:0.737494:0.414867:0.737494:0.414867:0.722580:0.406450:0.722580:0.000000
22:@0.414807:0.740378:0.424289:0.740378:0.424289:0.731668:0.414807:0.731668:0.000000:0.000000
, entonces   = :@0.430978:0.726828:0.545650:0.726828:0.545650:0.710395:0.430978:0.710395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λA:@0.509388:0.726828:0.526820:0.726828:0.526820:0.710422:0.509388:0.710422:0.000000:0.000000
a:@0.561797:0.716096:0.569394:0.716096:0.569394:0.701156:0.561797:0.701156:0.000000
11:@0.569320:0.718980:0.578803:0.718980:0.578803:0.710270:0.569320:0.710270:0.000000:0.000000
a:@0.604764:0.716096:0.612362:0.716096:0.612362:0.701156:0.604764:0.701156:0.000000
12:@0.612288:0.718980:0.621771:0.718980:0.621771:0.710270:0.612288:0.710270:0.000000:0.000000
a:@0.561797:0.737538:0.569394:0.737538:0.569394:0.722599:0.561797:0.722599:0.000000
21:@0.569320:0.740422:0.578803:0.740422:0.578803:0.731712:0.569320:0.731712:0.000000:0.000000
a:@0.604764:0.737538:0.612362:0.737538:0.612362:0.722599:0.604764:0.722599:0.000000
22:@0.612288:0.740422:0.621771:0.740422:0.621771:0.731712:0.612288:0.731712:0.000000:0.000000
. :@0.629700:0.726828:0.636934:0.726828:0.636934:0.710395:0.629700:0.710395:0.000000:0.000000
Ejercicio 5:@0.293660:0.768486:0.370805:0.768486:0.370805:0.751816:0.293660:0.751816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean   = :@0.293660:0.804321:0.361767:0.804321:0.361767:0.787887:0.293660:0.787887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.333070:0.804321:0.342955:0.804321:0.342955:0.787915:0.333070:0.787915:0.000000
1 2:@0.372754:0.793541:0.404783:0.793541:0.404783:0.778601:0.372754:0.778601:0.000000:0.000000:0.000000
–1 3:@0.368621:0.814986:0.404783:0.814986:0.404783:0.800046:0.368621:0.800046:0.000000:0.000000:0.000000:0.000000
,    = :@0.412625:0.804317:0.451295:0.804317:0.451295:0.787884:0.412625:0.787884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.423647:0.804317:0.432483:0.804317:0.432483:0.787911:0.423647:0.787911:0.000000
0 –1:@0.458465:0.795328:0.494644:0.795328:0.494644:0.780389:0.458465:0.780389:0.000000:0.000000:0.000000:0.000000
3 –5:@0.458465:0.816774:0.494644:0.816774:0.494644:0.801834:0.458465:0.801834:0.000000:0.000000:0.000000:0.000000
,    = :@0.502152:0.804317:0.541890:0.804317:0.541890:0.787884:0.502152:0.787884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.513175:0.804317:0.523078:0.804317:0.523078:0.787911:0.513175:0.787911:0.000000
3 4:@0.549794:0.794435:0.582542:0.794435:0.582542:0.779495:0.549794:0.779495:0.000000:0.000000:0.000000
3 –1:@0.549794:0.815880:0.586709:0.815880:0.586709:0.800940:0.549794:0.800940:0.000000:0.000000:0.000000:0.000000
. :@0.592746:0.804317:0.599980:0.804317:0.599980:0.787884:0.592746:0.787884:0.000000:0.000000
Halla x,      , si existen, tales que :@0.293660:0.850869:0.539666:0.850869:0.539666:0.834435:0.293660:0.834435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.348219:0.850869:0.355693:0.850869:0.355693:0.834463:0.348219:0.834463:0.000000
∈:@0.359576:0.850453:0.372701:0.850453:0.372701:0.833465:0.359576:0.833465:0.000000
ℝ:@0.376566:0.851452:0.389856:0.851452:0.389856:0.833797:0.376566:0.833797:0.000000
x  :@0.539434:0.850869:0.553368:0.850869:0.553368:0.834463:0.539434:0.834463:0.000000:0.000000:0.000000
1 2:@0.564371:0.841880:0.595328:0.841880:0.595328:0.826940:0.564371:0.826940:0.000000:0.000000:0.000000
–1 3:@0.560221:0.863325:0.595328:0.863325:0.595328:0.848386:0.560221:0.848386:0.000000:0.000000:0.000000:0.000000
 :@0.604256:0.850869:0.607569:0.850869:0.607569:0.834463:0.604256:0.834463:0.000000
 +   :@0.607502:0.850869:0.640985:0.850869:0.640985:0.834435:0.607502:0.834435:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.626296:0.850869:0.637009:0.850869:0.637009:0.834463:0.626296:0.834463:0.000000:0.000000
0 –1:@0.648155:0.840988:0.688852:0.840988:0.688852:0.826048:0.648155:0.826048:0.000000:0.000000:0.000000:0.000000
3 –5:@0.648155:0.862433:0.688852:0.862433:0.688852:0.847493:0.648155:0.847493:0.000000:0.000000:0.000000:0.000000
  =  :@0.691842:0.850869:0.718643:0.850869:0.718643:0.834435:0.691842:0.834435:0.000000:0.000000:0.000000:0.000000:0.000000
3 4:@0.725790:0.840094:0.757819:0.840094:0.757819:0.825154:0.725790:0.825154:0.000000:0.000000:0.000000
3 –1:@0.725790:0.861539:0.761969:0.861539:0.761969:0.846599:0.725790:0.846599:0.000000:0.000000:0.000000:0.000000
.:@0.769478:0.850869:0.772680:0.850869:0.772680:0.834435:0.769478:0.834435:0.000000
De las definiciones de producto de escalares por matrices, de la adición y de la igualdad :@0.293660:0.888954:0.931332:0.888954:0.931332:0.872520:0.293660:0.872520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de matrices se obtienen las siguientes equivalencias::@0.293660:0.905596:0.674364:0.905596:0.674364:0.889162:0.293660:0.889162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.293660:0.937853:0.304355:0.937853:0.304355:0.921447:0.293660:0.921447:0.000000:0.000000
 :@0.304300:0.937853:0.308331:0.937853:0.308331:0.921419:0.304300:0.921419:0.000000
1 2:@0.318371:0.927970:0.350751:0.927970:0.350751:0.913031:0.318371:0.913031:0.000000:0.000000:0.000000
–1 3:@0.314221:0.949416:0.350751:0.949416:0.350751:0.934476:0.314221:0.934476:0.000000:0.000000:0.000000:0.000000
  +    :@0.363932:0.937853:0.405314:0.937853:0.405314:0.921419:0.363932:0.921419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.390625:0.937853:0.401338:0.937853:0.401338:0.921447:0.390625:0.921447:0.000000:0.000000
0 –1:@0.414859:0.927970:0.453413:0.927970:0.453413:0.913031:0.414859:0.913031:0.000000:0.000000:0.000000:0.000000
3 –5:@0.414859:0.949416:0.453413:0.949416:0.453413:0.934476:0.414859:0.934476:0.000000:0.000000:0.000000:0.000000
  =  :@0.460917:0.937853:0.487718:0.937853:0.487718:0.921419:0.460917:0.921419:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.497238:0.927077:0.505404:0.927077:0.505404:0.912137:0.497238:0.912137:0.000000
4:@0.523460:0.927077:0.531626:0.927077:0.531626:0.912137:0.523460:0.912137:0.000000
3 –1:@0.497238:0.948522:0.535792:0.948522:0.535792:0.933583:0.497238:0.933583:0.000000:0.000000:0.000000:0.000000
  :@0.543296:0.937853:0.551285:0.937853:0.551285:0.921419:0.543296:0.921419:0.000000:0.000000
⇔ :@0.551198:0.937437:0.574888:0.937437:0.574888:0.920448:0.551198:0.920448:0.000000:0.000000
 :@0.574796:0.937853:0.578827:0.937853:0.578827:0.921419:0.574796:0.921419:0.000000
x 2x:@0.588867:0.927970:0.623824:0.927970:0.623824:0.913031:0.588867:0.913031:0.000000:0.000000:0.000000:0.000000
–x 3x:@0.584734:0.949416:0.623824:0.949416:0.623824:0.934476:0.584734:0.934476:0.000000:0.000000:0.000000:0.000000:0.000000
  +  :@0.634432:0.937853:0.661233:0.937853:0.661233:0.921419:0.634432:0.921419:0.000000:0.000000:0.000000:0.000000:0.000000
0 –y:@0.670753:0.927077:0.709877:0.927077:0.709877:0.912137:0.670753:0.912137:0.000000:0.000000:0.000000:0.000000
3y –5y:@0.667105:0.948522:0.713993:0.948522:0.713993:0.933583:0.667105:0.933583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  =  :@0.723926:0.937853:0.750727:0.937853:0.750727:0.921419:0.723926:0.921419:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.760247:0.927970:0.768413:0.927970:0.768413:0.913031:0.760247:0.913031:0.000000
4:@0.786469:0.927970:0.794635:0.927970:0.794635:0.913031:0.786469:0.913031:0.000000
3 –1:@0.760247:0.949416:0.798802:0.949416:0.798802:0.934476:0.760247:0.934476:0.000000:0.000000:0.000000:0.000000
.:@0.806305:0.937853:0.809508:0.937853:0.809508:0.921419:0.806305:0.921419:0.000000
La adición de matrices :@0.080953:0.179056:0.232387:0.179056:0.232387:0.164116:0.080953:0.164116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hereda las propiedades :@0.080953:0.194185:0.238474:0.194185:0.238474:0.179245:0.080953:0.179245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la adición de números :@0.080953:0.209314:0.251916:0.209314:0.251916:0.194374:0.080953:0.194374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales.:@0.080953:0.224443:0.121636:0.224443:0.121636:0.209503:0.080953:0.209503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades de  :@0.080953:0.246720:0.199328:0.246720:0.199328:0.231314:0.080953:0.231314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la adición:@0.080953:0.261849:0.149930:0.261849:0.149930:0.246443:0.080953:0.246443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La operación adición “+” :@0.080953:0.276978:0.242478:0.276978:0.242478:0.262038:0.080953:0.262038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en :@0.080953:0.292107:0.101569:0.292107:0.101569:0.277167:0.080953:0.277167:0.000000:0.000000:0.000000
M:@0.101485:0.292107:0.114102:0.292107:0.114102:0.277192:0.101485:0.277192:0.000000
2×2:@0.114039:0.294991:0.129297:0.294991:0.129297:0.286281:0.114039:0.286281:0.000000:0.000000:0.000000
[ ] satisface las :@0.129247:0.292107:0.233800:0.292107:0.233800:0.277167:0.129247:0.277167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.133615:0.292637:0.145696:0.292637:0.145696:0.276587:0.133615:0.276587:0.000000
siguientes propiedades::@0.080953:0.307236:0.237686:0.307236:0.237686:0.292296:0.080953:0.292296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conmutativa:@0.080953:0.329513:0.170484:0.329513:0.170484:0.314359:0.080953:0.314359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo  ,     :@0.080953:0.344642:0.189974:0.344642:0.189974:0.329702:0.080953:0.329702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.147554:0.344642:0.170931:0.344642:0.170931:0.329728:0.147554:0.329728:0.000000:0.000000:0.000000
∈:@0.174462:0.344264:0.186393:0.344264:0.186393:0.328820:0.174462:0.328820:0.000000
M:@0.189907:0.344642:0.202525:0.344642:0.202525:0.329728:0.189907:0.329728:0.000000
2×2:@0.202469:0.347525:0.217727:0.347525:0.217727:0.338815:0.202469:0.338815:0.000000:0.000000:0.000000
[ ],:@0.217677:0.344641:0.241322:0.344641:0.241322:0.329701:0.217677:0.329701:0.000000:0.000000:0.000000:0.000000
ℝ:@0.222044:0.345171:0.234126:0.345171:0.234126:0.329121:0.222044:0.329121:0.000000
 :@0.080953:0.359770:0.084617:0.359770:0.084617:0.344830:0.080953:0.344830:0.000000
A:@0.141195:0.359770:0.150181:0.359770:0.150181:0.344855:0.141195:0.344855:0.000000
 +   =   +  .:@0.150114:0.359770:0.229131:0.359770:0.229131:0.344830:0.150114:0.344830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.167199:0.359770:0.175231:0.359770:0.175231:0.344855:0.167199:0.344855:0.000000
B:@0.192250:0.359770:0.200282:0.359770:0.200282:0.344855:0.192250:0.344855:0.000000
A:@0.217300:0.359770:0.226286:0.359770:0.226286:0.344855:0.217300:0.344855:0.000000
Asociativa:@0.080936:0.374899:0.151190:0.374899:0.151190:0.359745:0.080936:0.359745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo :@0.080936:0.390028:0.147657:0.390028:0.147657:0.375088:0.080936:0.375088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B, C  M:@0.147537:0.390028:0.215978:0.390028:0.215978:0.375113:0.147537:0.375113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.187915:0.389650:0.199847:0.389650:0.199847:0.374206:0.187915:0.374206:0.000000
 :@0.199763:0.390028:0.203428:0.390028:0.203428:0.375088:0.199763:0.375088:0.000000
2×2:@0.215931:0.392912:0.231189:0.392912:0.231189:0.384202:0.215931:0.384202:0.000000:0.000000:0.000000
[ ],  :@0.231139:0.390028:0.260666:0.390028:0.260666:0.375088:0.231139:0.375088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.235507:0.390557:0.247588:0.390557:0.247588:0.374508:0.235507:0.374508:0.000000
A:@0.080953:0.405157:0.089939:0.405157:0.089939:0.390242:0.080953:0.390242:0.000000
 + (  +  ) = (  +  ) +  .:@0.089537:0.405157:0.229984:0.405157:0.229984:0.390217:0.089537:0.390217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B C:@0.109634:0.405157:0.142349:0.405157:0.142349:0.390242:0.109634:0.390242:0.000000:0.000000:0.000000
A B:@0.166078:0.405157:0.198776:0.405157:0.198776:0.390242:0.166078:0.390242:0.000000:0.000000:0.000000
C:@0.218472:0.405157:0.227474:0.405157:0.227474:0.390242:0.218472:0.390242:0.000000
Existencia de elemento :@0.080902:0.427434:0.243962:0.427434:0.243962:0.412280:0.080902:0.412280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
neutro:@0.080902:0.442563:0.127486:0.442563:0.127486:0.427409:0.080902:0.427409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.127473:0.442563:0.138243:0.442563:0.138243:0.427623:0.127473:0.427623:0.000000:0.000000:0.000000
Existe 0 = (0)    :@0.080902:0.457692:0.198314:0.457691:0.198314:0.442751:0.080902:0.442752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2×2:@0.163996:0.460575:0.179254:0.460575:0.179254:0.451865:0.163996:0.451865:0.000000:0.000000:0.000000
∈:@0.182802:0.457313:0.194733:0.457313:0.194733:0.441868:0.182802:0.441868:0.000000
M:@0.198247:0.457691:0.210864:0.457691:0.210864:0.442776:0.198247:0.442776:0.000000
2×2:@0.210789:0.460575:0.226047:0.460575:0.226047:0.451865:0.210789:0.451865:0.000000:0.000000:0.000000
[ ], :@0.225997:0.457691:0.253306:0.457691:0.253306:0.442751:0.225997:0.442751:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.230364:0.458220:0.242446:0.458220:0.242446:0.442171:0.230364:0.442171:0.000000
tal que para todo     :@0.080964:0.472820:0.226147:0.472820:0.226147:0.457880:0.080964:0.457880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.198034:0.472820:0.207021:0.472820:0.207021:0.457905:0.198034:0.457905:0.000000
∈:@0.210551:0.472442:0.222483:0.472442:0.222483:0.456997:0.210551:0.456997:0.000000
M:@0.080964:0.487949:0.093582:0.487949:0.093582:0.473034:0.080964:0.473034:0.000000
2×2:@0.093510:0.490833:0.108768:0.490833:0.108768:0.482123:0.093510:0.482123:0.000000:0.000000:0.000000
[ ],   + 0 = 0 +   = :@0.108717:0.487949:0.238321:0.487949:0.238321:0.473009:0.108717:0.473009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.113085:0.488478:0.125167:0.488478:0.125167:0.472429:0.113085:0.472429:0.000000
A:@0.135876:0.487949:0.144863:0.487949:0.144863:0.473034:0.135876:0.473034:0.000000
A:@0.212233:0.487949:0.221219:0.487949:0.221219:0.473034:0.212233:0.473034:0.000000
A.:@0.238238:0.487949:0.250186:0.487949:0.250186:0.473034:0.238238:0.473034:0.000000:0.000000
Existencia de opuestos :@0.080956:0.510226:0.241308:0.510226:0.241308:0.495072:0.080956:0.495072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aditivos.:@0.080956:0.525355:0.138259:0.525355:0.138259:0.510201:0.080956:0.510201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para cada     :@0.080956:0.540484:0.175368:0.540484:0.175368:0.525544:0.080956:0.525544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.147339:0.540484:0.156325:0.540484:0.156325:0.525569:0.147339:0.525569:0.000000
∈:@0.159856:0.540106:0.171787:0.540106:0.171787:0.524662:0.159856:0.524662:0.000000
M:@0.175301:0.540484:0.187919:0.540484:0.187919:0.525569:0.175301:0.525569:0.000000
2×2:@0.187850:0.543367:0.203108:0.543367:0.203108:0.534657:0.187850:0.534657:0.000000:0.000000:0.000000
[ ], :@0.203058:0.540483:0.230368:0.540483:0.230368:0.525543:0.203058:0.525543:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.207425:0.541012:0.219507:0.541012:0.219507:0.524963:0.207425:0.524963:0.000000
existe     :@0.080968:0.555612:0.149409:0.555612:0.149409:0.540672:0.080968:0.540672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.122334:0.555612:0.130366:0.555612:0.130366:0.540697:0.122334:0.540697:0.000000
∈:@0.133897:0.555233:0.145828:0.555233:0.145828:0.539789:0.133897:0.539789:0.000000
M:@0.149342:0.555612:0.161960:0.555612:0.161960:0.540697:0.149342:0.540697:0.000000
2×2:@0.161881:0.558496:0.177139:0.558496:0.177139:0.549786:0.161881:0.549786:0.000000:0.000000:0.000000
[ ], tal que :@0.177089:0.555612:0.253512:0.555612:0.253512:0.540672:0.177089:0.540672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.181456:0.556141:0.193538:0.556141:0.193538:0.540092:0.181456:0.540092:0.000000
A:@0.080953:0.570741:0.089939:0.570741:0.089939:0.555826:0.080953:0.555826:0.000000
 +   = 0.  :@0.089872:0.570741:0.150219:0.570741:0.150219:0.555801:0.089872:0.555801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.106957:0.570741:0.114989:0.570741:0.114989:0.555826:0.106957:0.555826:0.000000
Esta matriz está definida :@0.080936:0.593018:0.243950:0.593018:0.243950:0.578078:0.080936:0.578078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como   = (– ):@0.080936:0.608903:0.177586:0.608903:0.177586:0.593963:0.080936:0.593963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.123206:0.608903:0.131238:0.608903:0.131238:0.593989:0.123206:0.593989:0.000000
a:@0.160907:0.608903:0.169324:0.608903:0.169324:0.593989:0.160907:0.593989:0.000000
ij:@0.169291:0.611787:0.173183:0.611787:0.173183:0.603092:0.169291:0.603092:0.000000:0.000000
2×2:@0.177512:0.611787:0.192770:0.611787:0.192770:0.603077:0.177512:0.603077:0.000000:0.000000:0.000000
Propiedades del :@0.080953:0.631179:0.200260:0.631179:0.200260:0.615773:0.080953:0.615773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto de escalares :@0.080953:0.646308:0.241454:0.646308:0.241454:0.630902:0.080953:0.630902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por matrices:@0.080953:0.661437:0.170541:0.661437:0.170541:0.646031:0.080953:0.646031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.080953:0.683715:0.116874:0.683715:0.116874:0.668775:0.080953:0.668775:0.000000:0.000000:0.000000:0.000000:0.000000
A, B, C:@0.116780:0.683715:0.154237:0.683715:0.154237:0.668800:0.116780:0.668800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.154213:0.683715:0.173324:0.683715:0.173324:0.668775:0.154213:0.668775:0.000000:0.000000:0.000000
∈:@0.157811:0.683336:0.169742:0.683336:0.169742:0.667892:0.157811:0.667892:0.000000
M:@0.173257:0.683715:0.185874:0.683715:0.185874:0.668800:0.173257:0.668800:0.000000
2×2:@0.185795:0.686597:0.201053:0.686597:0.201053:0.677887:0.185795:0.677887:0.000000:0.000000:0.000000
[ ],:@0.201003:0.683713:0.224648:0.683713:0.224648:0.668774:0.201003:0.668774:0.000000:0.000000:0.000000:0.000000
ℝ:@0.205371:0.684243:0.217452:0.684243:0.217452:0.668194:0.205371:0.668194:0.000000
,      . Entonces:@0.088620:0.698842:0.200694:0.698842:0.200694:0.683902:0.088620:0.683902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.105751:0.698464:0.117682:0.698464:0.117682:0.683020:0.105751:0.683020:0.000000
ℝ:@0.121196:0.699372:0.133278:0.699372:0.133278:0.683323:0.121196:0.683323:0.000000
( A) =  A.   :@0.088606:0.721120:0.172388:0.721120:0.172388:0.705966:0.088606:0.705966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  )A =  A +  A.:@0.080953:0.736249:0.204360:0.736249:0.204360:0.721094:0.080953:0.721094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(A + B) =  A +  B.:@0.088606:0.751378:0.205245:0.751378:0.205245:0.736223:0.088606:0.736223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1A = A.:@0.080953:0.766506:0.130150:0.766506:0.130150:0.751352:0.080953:0.751352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M:@0.080953:0.788784:0.093570:0.788784:0.093570:0.773869:0.080953:0.773869:0.000000
2×2:@0.093510:0.791667:0.108768:0.791667:0.108768:0.782957:0.093510:0.782957:0.000000:0.000000:0.000000
[ ] es un espacio :@0.108718:0.788783:0.226507:0.788783:0.226507:0.773843:0.108718:0.773843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.113085:0.789312:0.125167:0.789312:0.125167:0.773263:0.113085:0.773263:0.000000
vectorial :@0.080956:0.804668:0.140870:0.804668:0.140870:0.789728:0.080956:0.789728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
real.:@0.140761:0.804826:0.168545:0.804826:0.168545:0.789139:0.140761:0.789139:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.138349:0.187141:0.138349:0.187141:0.121402:0.078581:0.121402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.154991:0.176057:0.154991:0.176057:0.138044:0.078581:0.138044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000